SOLUTION: A cistern can be filled by two pipes. The small pipe alone will take 24 minutes longer than the larger pipe to fill the cistern alone. The small pipe alone will take 32 minutes lon
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-> SOLUTION: A cistern can be filled by two pipes. The small pipe alone will take 24 minutes longer than the larger pipe to fill the cistern alone. The small pipe alone will take 32 minutes lon
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Question 1006498: A cistern can be filled by two pipes. The small pipe alone will take 24 minutes longer than the larger pipe to fill the cistern alone. The small pipe alone will take 32 minutes longer to fill the cistern alone when the two pipes are operating together. How long will it take for the larger pipe to fill the cistern alone? Found 2 solutions by josmiceli, MathTherapy:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Let = time in minutes for the larger pipe
to fill cistern when filling alone
Rate of filling =
Let = time in minutes for both pipes to
fill cistern when filling together
--------------------------- = time in minutes for smaller pipe to
fill cistern when filling alone
Rate of filling = = this is also time in minutes for smaller pipe to
fill cistern when filling alone
----------------------------
-----------------------------
Add their rates of filling alone to get rate filling together
Multiply both sides by
---------------------------------------------
Complete the square
The larger pipe takes 24 min filling alone
check:
OK
You can put this solution on YOUR website! A cistern can be filled by two pipes. The small pipe alone will take 24 minutes longer than the larger pipe to fill the cistern alone. The small pipe alone will take 32 minutes longer to fill the cistern alone when the two pipes are operating together. How long will it take for the larger pipe to fill the cistern alone?
Let time larger pipe takes be L
Then larger pipe can fill of cistern in 1 minute
Smaller pipe can fill cistern in (L + 24) mins, or of cistern in 1 minute
Since smaller pipe takes 32 minutes longer to fill cistern than when both pipes are on, then the time it
takes to fill cistern when both are on = L + 24 – 32, or L – 8 minutes. Both can fill of cistern in 1 min
The following 1-minute RATES equation is thus formed:
(L + 24)(L – 8) + L(L – 8) = L(L + 24) -------- Multiplying by LCD, L(L + 24)(L – 8)
(L - 24)(L + 8) = 0
L, or time larger pipe takes = minutes OR L = - 8 (ignore)
